{
  "id": "2102.02497",
  "version": "v1",
  "published": "2021-02-04T09:15:41.000Z",
  "updated": "2021-02-04T09:15:41.000Z",
  "title": "A Rauzy fractal unbounded in all directions of the plane",
  "authors": [
    "Mélodie Andrieu"
  ],
  "categories": [
    "math.DS",
    "math.CO"
  ],
  "abstract": "We construct an Arnoux-Rauzy word for which the set of all differences of two abelianized factors is equal to $\\mathbb{Z}^3$. In particular, the imbalance of this word is infinite - and its Rauzy fractal is unbounded in all directions of the plane.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-04T09:15:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "rauzy fractal",
      "directions",
      "arnoux-rauzy word",
      "differences"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}